Research papers in lightweight cryptography for the Constrained Application Protocol (CoAP) primarily address the challenge of securing IoT communication while considering the strict resource limitations of Low-Power and Lossy Networks (LLNs). Since CoAP operates over UDP and is widely used in constrained IoT environments, traditional cryptographic mechanisms such as TLS/DTLS often introduce significant computational, memory, and energy overhead, making them unsuitable for battery-powered sensor nodes. To overcome this, researchers have developed and evaluated lightweight cryptographic schemes tailored to CoAP, focusing on maintaining confidentiality, integrity, authentication, and replay protection with minimal resource consumption. Symmetric-key cryptography approaches using block ciphers like AES-CCM, PRESENT, and SPECK are commonly applied due to their reduced complexity and efficiency. Public-key mechanisms such as Elliptic Curve Cryptography (ECC), particularly ECDH and ECDSA, are explored for key exchange and digital signatures, providing strong security with smaller key sizes compared to RSA. Certificate-less and identity-based cryptography have also been investigated to reduce key management complexity in CoAP deployments. Furthermore, several studies explore the integration of lightweight Object Security solutions like OSCORE (Object Security for Constrained RESTful Environments), which apply end-to-end encryption and integrity protection directly at the CoAP message layer, thus lowering session overhead compared to DTLS. Proxy-assisted and hardware-accelerated lightweight cryptography techniques are also reported to offload security tasks while preserving device energy. Recent works combine lightweight cryptography with emerging paradigms such as blockchain-based trust management, group communication security, and machine learning-driven adaptive encryption to balance security and performance. Despite progress, open challenges remain in achieving resistance against evolving threats, ensuring interoperability across heterogeneous IoT devices, and designing ultra-lightweight yet robust cryptographic protocols that scale in large CoAP-based networks. Overall, the literature emphasizes that lightweight cryptography is a critical enabler for securing CoAP while preserving the efficiency and scalability required in real-world IoT applications.